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Section 2.3 – The Derivative Function Section 2.3.1 – The Graph of the First Derivative Function.

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Presentation on theme: "Section 2.3 – The Derivative Function Section 2.3.1 – The Graph of the First Derivative Function."— Presentation transcript:

1 Section 2.3 – The Derivative Function Section 2.3.1 – The Graph of the First Derivative Function

2 This is the graph of f(x). This is the graph of f ‘ (x). How do we get this? f(x) inc f ‘ (x) pos f(x) dec f ‘ (x) neg

3 This is the graph of f(x). This is the graph of f ‘ (x).

4 Steps to Graphing The First Derivative 1. Graph the x-intercepts (slope of tangent is zero) 2. Mark points of inflection (opening up/down changes) 3.Analyze trends of slopes and fill in shapes. Note: the y-axis of the derivative graph is no longer a y-coordinate, but a VALUE OF SLOPE

5 Example of Graphs of First Derivative

6

7 This is the graph of f(x) Graph f ‘ (x).

8

9

10 Section 2.3.2 – The Derivative Function

11 Use the results to sketch a graph of f ‘ over the interval [0, 3]

12

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